Free Printable Confidence Interval for Means using z

1.

A sample of 20 cupcakes found the interval for average calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

a)

We are 95% confident that the true mean caloric content can be found with a sample of 150 to 350 cupcakes.

b)

We are 95% confident that the interval (150, 350) captures the true average caloric content.

c)

We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

d)

None of these are correct.

2.

Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.

a)

89.08 < μ < 94.92

b)

87.27 < μ < 96.73

c)

87.29 < μ < 96.71

d)

87.77 < μ < 96.23

3.

Which of the following changes to a study would result in a narrower confidence interval?

a)

increasing the confidence level, increasing the sample size

b)

decreasing the confidence level, decreasing the sample size

c)

increasing the confidence level, decreasing the sample size

d)

decreasing the confidence level, increasing the sample size.

4.

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the critical value.

a)

0.90

b)

1.155

c)

1.645

d)

±1.645

5.

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

a)

(114.5, 125.6)

b)

(112.8, 127.4)

c)

(112.82, 127.38)

d)

(114.56, 125.64)

6.

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

a)

1.799

b)

1.798

c)

1.803

7.

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

What is the point estimate?

a)

75

b)

105.2

c)

10

d)

0.90

8.

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the Standard Error.

a)

75

b)

10

c)

105.2

d)

1.155

9.

Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

a)

90%

b)

95%

c)

98%

d)

99%

10.

A research company wants to estimate the proportion of people who like oatmeal. They want the confidence level to be 95%. The company gets 325 people to sign up for the survey, but on the day that the survey is issued, only 250 people show up and take the survey. What happens to the confidence interval?

a)

It gets larger

b)

It gets smaller

c)

It stays the same

d)

Too little information given

11.

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

a)

1.799

b)

1.798

c)

1.803

Confidence Interval for Means using z

Total questions: 11

Worksheet time: 27mins

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